Staircase Structure Research Articles

Eigenspectrum, Chern numbers and phase diagrams of ultracold color-orbit-coupled SU(3) fermions in optical lattices

We study ultracold color fermions with three internal states Red, Green and Blue with ${\rm SU(3)}$ symmetry in optical lattices, when color-orbit coupling and color-flip fields are present. This system corresponds to a generalization of two-internal state fermions with ${\rm SU(2)}$ symmetry in the presence of spin-orbit coupling and spin-flipping Zeeman fields. We investigate the eigenspectrum and Chern numbers to describe different topological phases that emerge in the phase diagrams of color-orbit coupled fermions in optical lattices. We obtain the phases as a function of artificial magnetic, color-orbit and color-flip fields that can be independently controlled. For fixed artificial magnetic flux ratio, we identify topological quantum phases and phase transitions in the phase diagrams of chemical potential versus color-flip fields or color-orbit coupling, where the chirality and number of midgap edge states changes. The topologically non-trivial phases are classified in three groups: the first group has total non-zero chirality and exhibit only the quantum charge Hall effect; the second group has total non-zero chirality and exhibit both quantum charge and quantum color Hall effects; and the third group has total zero chirality, but exhibit the quantum color Hall effect. These phases are generalizations of the quantum Hall and quantum spin Hall phases for charged spin-$1/2$ fermions. Lastly, we also describe the color density of states and a staircase structure in the total and color filling factors versus chemical potential for fixed color-orbit, color-flip and magnetic flux ratio. We show the existence of incompressible states at rational filling factors precisely given by a gap-labelling theorem that relates the filling factors to the magnetic flux ratio and topological quantum numbers.

A unified theory of zonal flow shears and density corrugations in drift wave turbulence

A unified theory of zonal flow shears and density corrugations in drift wave turbulence is presented. Polarization and density advection beat excitation are studied in combination with modulational response. Noise is driven by two-time flux correlation. While the effective zonal flow eddy viscosity can go negative, the zonal diffusivity is positive definite. There is no inverse cascade of density corrugation. The connection between avalanches and corrugations is discussed. The zonal cross-correlation is identified and calculated. Conditions for alignment of zonal shears and corrugation gradients are determined, and the implications for staircase structure are discussed. We show that the synergy of beat noise and modulational effects is stronger than either alone. Strong zonal flows can be excited well below the modulational instability threshold. In the context of L–H transition, zonal noise quenches turbulence overshoot by eliminating the threshold for zonal flow excitation. The power threshold for L–H transition is lowered.

Loss of Baiap2l2 destabilizes the transducing stereocilia of cochlear hair cells and leads to deafness.

Key points Mechanoelectrical transduction at auditory hair cells requires highly specialized stereociliary bundles that project from their apical surface, forming a characteristic graded ‘staircase’ structure.The morphogenesis and maintenance of these stereociliary bundles is a tightly regulated process requiring the involvement of several actin‐binding proteins, many of which are still unidentified.We identify a new stereociliary protein, the I‐BAR protein BAIAP2L2, which localizes to the tips of the shorter transducing stereocilia in both inner and outer hair cells (IHCs and OHCs).We find that Baiap2l2 deficient mice lose their second and third rows of stereocilia, their mechanoelectrical transducer current, and develop progressive hearing loss, becoming deaf by 8 months of age.We demonstrate that BAIAP2L2 localization to stereocilia tips is dependent on the motor protein MYO15A and its cargo EPS8.We propose that BAIAP2L2 is a new key protein required for the maintenance of the transducing stereocilia in mature cochlear hair cells. The transduction of sound waves into electrical signals depends upon mechanosensitive stereociliary bundles that project from the apical surface of hair cells within the cochlea. The height and width of these actin‐based stereocilia is tightly regulated throughout life to establish and maintain their characteristic staircase‐like structure, which is essential for normal mechanoelectrical transduction. Here, we show that BAIAP2L2, a member of the I‐BAR protein family, is a newly identified hair bundle protein that is localized to the tips of the shorter rows of transducing stereocilia in mouse cochlear hair cells. BAIAP2L2 was detected by immunohistochemistry from postnatal day 2.5 (P2.5) throughout adulthood. In Baiap2l2 deficient mice, outer hair cells (OHCs), but not inner hair cells (IHCs), began to lose their third row of stereocilia and showed a reduction in the size of the mechanoelectrical transducer current from just after P9. Over the following post‐hearing weeks, the ordered staircase structure of the bundle progressively deteriorates, such that, by 8 months of age, both OHCs and IHCs of Baiap2l2 deficient mice have lost most of the second and third rows of stereocilia and become deaf. We also found that BAIAP2L2 interacts with other key stereociliary proteins involved in normal hair bundle morphogenesis, such as CDC42, RAC1, EPS8 and ESPNL. Furthermore, we show that BAIAP2L2 localization to the stereocilia tips depends on the motor protein MYO15A and its cargo EPS8. We propose that BAIAP2L2 is key to maintenance of the normal actin structure of the transducing stereocilia in mature mouse cochlear hair cells.

Diffraction efficiency of a small-period astronomical x-ray reflection grating fabricated using thermally activated selective topography equilibration

We have fabricated a blazed x-ray reflection grating with a period of 160 nm using thermally activated selective topography equilibration (TASTE) and electron-beam (ebeam) physical vapor evaporation. TASTE makes use of grayscale ebeam lithography to create three-dimensional (3-D) structures in resist, which can then be thermally reflown into a desired profile. A blazed grating profile can be fabricated by selectively reflowing a periodic staircase structure into a wedge. This was done for the first time at a grating period of 160 nm, 2.5 times smaller than previous x-ray gratings fabricated using TASTE. The grating was patterned over a 10 mm by 60 mm area in a 147-nm-thick layer of poly(methyl methacrylate) resist and coated with 5 nm of chromium and 15 nm of gold using ebeam evaporation. The diffraction efficiency of the grating was measured using beamline 6.3.2 at Lawrence Berkeley National Laboratory’s Advanced Light Source. The results show a total absolute diffraction efficiency ≳40 % at lower energies, with maximum single-order diffraction efficiency ranging from 20% to 40%. The total diffraction efficiency was ≳30 % across the measured bandpass of 180 to 1300 eV.

Study on seismic performance of frame structure with viscous damping staircase

Based on the significant energy dissipation performance of the viscous damper, the force-displacement hysteresis curve is full and the Maxwell mechanical model has a weak dependence on vibration frequency. Combining the failure mode of the staircase damage with the Maxwell mechanical model, this paper proposes an earthquake-resistant frame staircase model with damped bearings. A finite element analysis of a nine-story reinforced concrete structure is performed using SAP2000. By setting three different connection methods on the staircase structure, the similarities and differences of different staircase structures to the input seismic wave feedback are analyzed to compare the advantages and disadvantages of its seismic performance.

Climbing up the memory staircase: Equatorial zoom-whirl orbits

The nonlinear, or null gravitational memory effect for zoom-whirl orbits around fast spinning Kerr black holes for extreme mass ratio systems has a staircase structure. The latter is characterized by a periodic fast increase in the memory during the whirl phases of the orbit, and near constant levels when the orbit is near apoapsis. We study the contribution of different spherical harmonic modes to this effect, and discuss the relative importance thereof. Because the hereditary memory effect increases in magnitude linearly in the number of periapsis passages on a dynamical time scale, while the oscillatory parent gravitational waves are sourced by an orbit that evolves on a much longer radiation reaction time scale, the magnitude of the former relative to the latter increases with time. We also consider orphan memory and the memory effect for extreme mass ratio inspirals. We then discuss the prospect of detection with the Laser Interferometer Space Antenna (LISA).

Analysis of Acoustic Observations of Double‐Diffusive Finestructure in the Arctic Ocean

AbstractDouble‐diffusive convection may occur if both temperature and salinity increase with depth, as in the Arctic Ocean. The process is identifiable by a staircase structure, with mixed layers separated by high‐gradient interfaces in temperature and salinity. These staircases, which persist if turbulence levels are weak, are widely present in the Arctic Ocean and responsible for transporting heat toward the overlying sea ice. Acoustic observations (reflection coefficients) from a broadband echo sounder are analyzed here to track the detailed evolution of interfaces in the Arctic's double‐diffusive staircase. We infer interface thicknesses from reflection coefficient profiles and find that thicknesses appear to be related to water column displacements. Further, we relate reflection coefficients to interface stratification and interpret stratification changes in the context of turbulence acting to thicken interfaces. The high‐resolution capabilities of the echo sounder allow for insights into how double‐diffusive heat fluxes and inferred mixing levels may vary in space/time.

Analyzing the Influencing Factors of Marine Fishery Market Power by Using the ISM Model

Wu, C.; Tan, L.; Han, J., and Liu, Z., 2020. Analyzing the influencing factors of marine fishery market power by using the ISM model. In: Gong, D.; Zhang, M., and Liu, R. (eds.), Advances in Coastal Research: Engineering, Industry, Economy, and Sustainable Development. Journal of Coastal Research, Special Issue No. 106, pp. 161–165. Coconut Creek (Florida), ISSN 0749-0208.This paper analyzes the main factors that influence the marine fishery market power and establishes the interpretive structural modeling (ISM) model to obtain a five-layer staircase structure of these factors. This paper also analyzes the factors using MICMAC and draws conclusions. First, technological innovation is one of the ultimate risk factors, which should be considered as intervention factor and used to produce specific control strategy. Second, entry barriers, industrial support policies, and administrative monopoly systems are the most fundamental factors, which are strongly driven and weakly dependent but have a higher influence on other factors. Third, natural resources and sociometric resource factors have less influence on marine fishery market power.

An Improved Dimensional Measurement Method of Staircase Patterns With Higher Precision in 3D NAND

3D NAND is a great architectural innovation in the field of flash memory. The staircase for control gate is a unique and important process in the manufacturing of 3D NAND. The staircase is employed to form the electrical connection between the control gate and contact. The current method used to measure the dimension of staircase patterns is, however, not precise enough for the development of state-of-the-art 3D NAND. In this circumstance, an accurate measurement of dimension for as-formed staircase patterns is of great importance and technical interest. In this paper, an improved measurement method is proposed to meet the requirement for higher precision. By taking the overlay into account, a calculation formula for measuring the dimensional error of as-formed staircase is derived for the first time. Two kinds of anchor design (convex SS0 and concave SS0) are put forward to perform dedicated experiments. Achieved results show that the measurement error of as-formed staircase using this improved method is improved from 31.6 nm for normal measurement method to 14.1 nm. The dimensional uniformity of as-formed staircase is therefore improved significantly which in turn leads to well controlled word line leakage. Furthermore, in advanced staircase structure of stair divided scheme (SDS), the convex SS0 shows an advantage in cost compared to the concave SS0.

Microwave induced tunable subharmonic steps in superconductor–ferromagnet–superconductor Josephson junction

We investigate the coupling between ferromagnet and superconducting phase dynamics in superconductor-ferromagnet-superconductor Josephson junction. The current-voltage characteristics of the junction demonstrate a pattern of subharmonic current steps which forms a devil's staircase structure. We show that a width of the steps becomes maximal at ferromagnetic resonance. Moreover, we demonstrate that the structure of the steps and their widths can be tuned by changing the frequency of the external magnetic field, ratio of Josephson to magnetic energy, Gilbert damping and the junction size.

Attractors of trees of maps and of sequences of maps between spaces with applications to subdivision

An extension of the Banach fixed-point theorem for a sequence of maps on a complete metric space (X, d) has been presented in a previous paper. It has been shown that backward trajectories of maps $$X\rightarrow X$$ converge under mild conditions and that they can generate new types of attractors such as scale-dependent fractals. Here we present two generalizations of this result and some potential applications. First, we study the structure of an infinite tree of maps $$X\rightarrow X$$ and discuss convergence to a unique “attractor” of the tree. We also consider “staircase” sequences of maps, that is, we consider a countable sequence of metric spaces $$\{(X_i,d_i)\}$$ and an associated countable sequence of maps $$\{T_i\}$$, $$T_i:X_{i}\rightarrow X_{i-1}$$. We examine conditions for the convergence of backward trajectories of the $$\{T_i\}$$ to a unique attractor. An example of such trees of maps are trees of function systems leading to the construction of fractals which are both scale-dependent and location dependent. The staircase structure facilitates linking all types of linear subdivision schemes to attractors of function systems.

Formation of a High Pressure Staircase Pedestal with Suppressed Edge Localized Modes in the DIII-D Tokamak.

We observe the formation of a high-pressure staircase pedestal (≈16-20 kPa) in the DIII-D tokamak when large amplitude edge localized modes are suppressed using resonant magnetic perturbations. The staircase pedestal is characterized by a flattening of the density and temperature profiles in midpedestal creating a two-step staircase pedestal structure correlated with the appearance of midpedestal broadband fluctuations. The pedestal oscillates between the staircase and single-step structure every 40-60ms, correlated with oscillations in the heat and particle flux to the divertor.Gyrokinetic analysis using the cgyro code shows that when the heat and particle flux to the divertor decreases, the pedestal broadens and the E×B shear at the midpedestal decreases, triggering a transport bifurcation from the kinetic ballooning mode (KBM) to trapped electron mode (TEM) limited transport that flattens the density and temperature profiles at midpedestal and results in the formation of the staircase pedestal. As the heat flux to the divertor increases, the pedestal narrows and the E×B shear at the midpedestal increases, triggering a back transition from TEM to KBM limited transport. The pedestal pressure increases during the staircase phase, indicating that enhanced midpedestal turbulence can be beneficial for confinement.

Dynamics of the boundary layer created by the explosion of a dense object in an ambient dilute gas triggered by a high power laser

The dynamics of the boundary layer in between two distinct collisionless plasmas created by the interaction between a dense object modeling a cluster and a short laser pulse in the presence of an ambient gas is studied with two dimensional relativistic particle-in-cell simulations, which are found to be described by three successive processes. In the first phase, a collisionless electrostatic shock wave, launched near the cluster expansion front, reflects the ambient gas ions at a contact surface as a moving wall, which allows a particle acceleration with a narrower energy spread. In the second phase, the contact surface disappears and the compressed surface of the ambient gas ions passes over the shock potential, forming an overlapping region between the cluster expansion front and the compressed surface of the ambient gas. Here, another type of nonlinear wave is found to be evolved, leading to a relaxation of the shock structure, while continuing to reflect the ambient gas ions. The nonlinear wave exhibits a bipolar electric field structure that is sustained for a long timescale coupled with slowly evolving ion dynamics, suggesting that a quasistationary kinetic equilibrium dominated by electron vortices in the phase space is established. In the third phase, a rarefaction wave is triggered and evolves at the compressed surface of ambient gas. This is because some of the ambient gas ions tend to pass over the potential of the bipolar electric field. Simultaneously, a staircase structure, i.e., a kind of internal shock, is formed in the cluster due to the deceleration of cluster ions. Such structure formations and successive dynamics accompanied by the transitions from the shock wave phase through the overlapping phase to the rarefaction wave phase are considered to be a unique nature at the boundary layer created by an explosion of a dense plasma object in an ambient dilute plasma.

Renormalized perturbation approach to instanton-noninstanton transition in nearly integrable tunneling processes.

A renormalized perturbation method is developed for quantum maps of periodically kicked rotor models to study the tunneling effect in the nearly integrable regime. Integrable Hamiltonians closely approximating the nonintegrable quantum map are systematically generated by the Baker-Hausdorff-Campbell (BHC) expansion for symmetrized quantum maps. The procedure results in an effective integrable renormalization, and the unrenormalized residual part is treated as the perturbation. If a sufficiently high-order BHC expansion is used as the base of perturbation theory, the lowest order perturbation well reproduces tunneling characteristics of the quasibound eigenstates, including the transition from the instanton tunneling to a noninstanton one. This approach enables a comprehensive understanding of the purely quantum mechanisms of tunneling in the nearly integrable regime. In particular, the staircase structure of tunneling probability dependence on quantum number can be clearly explained as the successive transition among multiquanta excitation processes. The transition matrix elements of the residual interaction have resonantly enhanced invariant components that are not removed by the renormalization. Eigenmodes coupled via these invariant components form noninstanton (NI) tunneling channels of two types contributing to the two regions of each step of the staircase structure: one type of channel is inside the separatrix, and the other goes across the separatrix. The amplitude of NI tunneling across the separatrix is insensitive to the Planck constant but shows an essentially singular dependence upon the nonintegrablity parameter. Its relation to the Melnikov integral, which characterizes the scale of classical chaos emerging close to the saddle on the potential top, is discussed.

Chern-number spectrum of ultracold fermions in optical lattices tuned independently via artificial magnetic, Zeeman, and spin-orbit fields

We discuss the Chern number spectrum of ultra-cold fermions in square optical lattices as a function of artificial magnetic, Zeeman and spin-orbit fields that can be tuned independently. We show the existence of topological quantum phase transitions induced by Zeeman and spin-orbit fields, where the total number and chirality of edge states change for fixed magnetic flux ratio, thus leading to topological-insulator phases which are different from those found at zero Zeeman and spin-orbit fields. We construct phase diagrams of chemical potential versus Zeeman field or spin-orbit coupling and characterize all insulating phases by their topological invariants. Lastly, we obtain a staircase structure in the filling factor versus chemical potential for various Zeeman and spin-orbit fields, showing the existence of incompressible states at rational filling factors derived from a generalized Diophantine equation.

Perfluorophenyl-Directed Giant Porphyrin J-Aggregates.

Quadrupolar interactions of porphyrin bearing two pentafluorophenylethynyl terminals (1) drove the formation of a successive one-dimensional staircase structure, i.e., J-aggregates, to yield millimeter-length needles with a single-crystalline character in methylcyclohexane solution. In contrast, π-stacked interactions of porphyrin bearing two nonfluorinated phenyl terminals (2) formed no aggregates in solution. A spin-cast film of 1 also showed bathochromic shift of the Soret and Q bands, indicating the formation of J-aggregates. The molecular arrangement of the J-aggregates was revealed by microbeam glazing-incidence wide-angle X-ray diffraction (GIWAXD), and was in good agreement with the optimized structure generated by density functional theory (DFT) calculations.

Dynamics of potential vorticity staircase evolution and step mergers in a reduced model of beta-plane turbulence

A two-field model of potential vorticity (PV) staircase structure and dynamics relevant to both beta-plane and drift-wave plasma turbulence is studied numerically and analytically. The model evolves averaged PV whose flux is both driven by and regulates, a potential enstrophy field, $\varepsilon$. The model employs a closure using a mixing length model. Its link to bistability, vital to staircase generation, is analyzed and verified by integrating the equations numerically. Long-time staircase evolution consistently manifests a pattern of meta-stable quasi-periodic configurations, lasting for hundreds of time units, yet interspersed with abrupt ($\Delta t\ll1$) mergers of adjacent steps in the staircase. The mergers occur at the staircase lattice defects where the pattern has not completely relaxed to a strictly periodic solution that can be obtained analytically. Other types of stationary solutions are solitons and kinks in the PV gradient and $\varepsilon$ - profiles. The waiting time between mergers increases strongly as the number of steps in the staircase decreases. This is because of an exponential decrease in inter-step coupling strength with growing spacing. The long-time staircase dynamics is shown numerically be determined by local interaction with adjacent steps. Mergers reveal themselves through the explosive growth of the turbulent PV-flux which, however, abruptly drops to its global constant value once the merger is completed.

Long frontal waves and dynamic scaling in freely evolving equivalent barotropic flow

We present a scaling theory that links the frequency of long frontal waves to the kinetic energy decay rate and inverse transfer of potential energy in freely evolving equivalent barotropic turbulence. The flow energy is predominantly potential, and the streamfunction makes the dominant contribution to potential vorticity (PV) over most of the domain, except near PV fronts of width $O(L_{D})$, where $L_{D}$ is the Rossby deformation length. These fronts bound large vortices within which PV is well-mixed and arranged into a staircase structure. The jets collocated with the fronts support long-wave undulations, which facilitate collisions and mergers between the mixed regions, implicating the frontal dynamics in the growth of potential-energy-containing flow features. Assuming the mixed regions grow self-similarly in time and using the dispersion relation for long frontal waves (Nycander et al., Phys. Fluids A, vol. 5, 1993, pp. 1089–1091) we predict that the total frontal length and kinetic energy decay like $t^{-1/3}$, while the length scale of the staircase vortices grows like $t^{1/3}$. High-resolution simulations confirm our predictions.

Light-cone and local front dynamics of a single-particle extended quantum walk

We study the light-cone and front dynamics of a single particle continuous time extended quantum walk on a one dimensional lattice with finite range hopping. We show that, in general, for an initially localized state, propagating wave fronts can be characterized as ordinary or extremal fronts with the latter exhibiting an anomalous sub-diffusive scaling behaviour in the front region. We investigate the dynamical global and local scaling properties of the cumulative probability distribution function for the extended walk with nearest and next-nearest neighbour hopping using analytical and numerical methods. The global scaling shows the existence of a 'causal light-cone' corresponding to excitations travelling with a velocity smaller than a maximal 'light velocity'. Maximal fronts moving with fixed 'light velocity' bound the causal cone. The front regions spread with time sub-diffusively exhibiting a local Airy scaling which leads to an internal staircase structure. At a certain critical next-nearest neighbour hopping strength, there is a transition from a phase with one 'causal cone' to a phase with two nested 'causal cones' and the existence of an internal staircase structure in the corresponding cumulative distribution profiles. We also connect the study to that in spin chain systems and indicate that a single particle quantum walk on the one dimensional lattice already captures the many body physics of a spin chain system. In particular, we suggest that the time evolution of a single particle quantum walk on the one dimensional lattice with an initially localized state is equivalent to the time evolution of a domain wall initial state in a corresponding spin chain system.

Low temperature thermoluminescence of Gd2O3 nanoparticles using various heating rate and Tmax − Texc. methods

Abstract Thermoluminescence (TL) measurements for Gd2O3 nanoparticles were carried out for various heating rates between 0.3 and 0.8 K/s at low temperatures (10–280 K). TL spectrum exhibited two observable and one faint peaks in the temperature region of 10–100 K, and four peaks in the temperature region of 160–280 K. Heating rate analysis was achieved to understand the behaviors of trap levels. It was seen that the peak maximum temperatures and TL intensities of all peaks increase with increasing heating rate. This behavior was ascribed to anomalous heating rate effect. Tmax − Texc. analysis was accomplished for TL peaks at relatively higher temperature region to reveal the related traps depths. Tmax − Texc. plot presented a staircase structure indicating that the TL glow curve is composed of well separated glow peaks. Mean activation energies of trapping centers corresponding to these separated peaks were found as 0.43, 0.50, 0.58 and 0.80 eV.